Solve Equations with Supplementary Angles Quick Check

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Question
∠ACB
and ∠BCD
are supplementary angles. The angles have the following measures: ∡ACB=(x+28)°
and ∡BCD=(x+48)°
. What is m∠BCD
?(1 point)
Responses

52°
52 degrees

100°
100 degrees

128°
128 degrees

80°
80 degrees
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1 answer

Since angles ACB and BCD are supplementary, their measures add up to 180 degrees.

Given:

  • m∠ACB = (x + 28)°
  • m∠BCD = (x + 48)°

We can set up the equation:

\[ m∠ACB + m∠BCD = 180° \]

Substituting in the expressions for the angles:

\[ (x + 28) + (x + 48) = 180 \]

Combining like terms:

\[ 2x + 76 = 180 \]

Now, subtract 76 from both sides:

\[ 2x = 104 \]

Dividing both sides by 2 gives:

\[ x = 52 \]

Now, substituting \(x\) back into the expression for m∠BCD:

\[ m∠BCD = x + 48 = 52 + 48 = 100° \]

Therefore, the correct answer is:

100°.